

# DISCLAIMER: This file is strongly influenced by https://github.com/ermongroup/ddim

from dataclasses import dataclass
from typing import Optional, Tuple, Union

import flax
import jax
import jax.numpy as jnp

from ..configuration_utils import ConfigMixin, register_to_config
from .scheduling_utils_flax import (
    CommonSchedulerState,
    FlaxKarrasDiffusionSchedulers,
    FlaxSchedulerMixin,
    FlaxSchedulerOutput,
    add_noise_common,
    get_velocity_common,
)






@flax.struct.dataclass
class      lowerCamelCase_      :
	_lowercase		:   CommonSchedulerState

	# setable values
	_lowercase		:   jnp.ndarray
	_lowercase		:   jnp.ndarray
	_lowercase		:   Optional[int]     					=				None




	@classmethod
	def        lowerCAmelCase_       (     cls						:     Any					,      __A						:     CommonSchedulerState					,      __A						:     jnp.ndarray					,      __A						:     jnp.ndarray							):
		return cls(common=__A					,      init_noise_sigma=__A					,      timesteps=__A							)






@dataclass
class      lowerCamelCase_      (	_lowercase	):
	_lowercase		:   DDPMSchedulerState






class      lowerCamelCase_      (	_lowercase						,      _lowercase	):
	_lowercase		:   Optional[int]     					=				[e.name for e in FlaxKarrasDiffusionSchedulers]

	_lowercase		:   jnp.dtype




	@property
	def        lowerCAmelCase_       (     self						:     Tuple							):
		return True




	@register_to_config
	def __init__(     self						:     str					,      __A						:     int = 1000					,      __A						:     float = 0.0_0_0_1					,      __A						:     float = 0.0_2					,      __A						:     str = "linear"					,      __A						:     Optional[jnp.ndarray] = None					,      __A						:     str = "fixed_small"					,      __A						:     bool = True					,      __A						:     str = "epsilon"					,      __A						:     jnp.dtype = jnp.floataa					,      ):
		__A :			Dict		    =			dtype




	def        lowerCAmelCase_       (     self						:     Optional[Any]					,      __A						:     Optional[CommonSchedulerState] = None							):
		if common is None:
			__A :			List[str]		    =			CommonSchedulerState.create(self							)

		# standard deviation of the initial noise distribution
		__A :			Any		    =			jnp.array(1.0					,      dtype=self.dtype							)

		__A :			Any		    =			jnp.arange(0					,      self.config.num_train_timesteps							).round()[::-1]

		return DDPMSchedulerState.create(
		    common=__A					,      init_noise_sigma=__A					,      timesteps=__A					,      )




	def        lowerCAmelCase_       (     self						:     Any					,      __A						:     DDPMSchedulerState					,      __A						:     jnp.ndarray					,      __A						:     Optional[int] = None							):
		return sample




	def        lowerCAmelCase_       (     self						:     Dict					,      __A						:     DDPMSchedulerState					,      __A						:     int					,      __A						:     Tuple = ()							):
		__A :			Dict		    =			self.config.num_train_timesteps // num_inference_steps
		# creates integer timesteps by multiplying by ratio
		# rounding to avoid issues when num_inference_step is power of 3
		__A :			Dict		    =			(jnp.arange(0					,      __A							) * step_ratio).round()[::-1]

		return state.replace(
		    num_inference_steps=__A					,      timesteps=__A					,      )




	def        lowerCAmelCase_       (     self						:     Optional[int]					,      __A						:     DDPMSchedulerState					,      __A						:     List[str]					,      __A						:     Union[str, Any]=None					,      __A						:     List[str]=None							):
		__A :			Dict		    =			state.common.alphas_cumprod[t]
		__A :			Tuple		    =			jnp.where(t > 0					,      state.common.alphas_cumprod[t - 1]					,      jnp.array(1.0					,      dtype=self.dtype							)							)

		# For t > 0, compute predicted variance βt (see formula (6) and (7) from https://arxiv.org/pdf/2006.11239.pdf)
		# and sample from it to get previous sample
		# x_{t-1} ~ N(pred_prev_sample, variance) == add variance to pred_sample
		__A :			List[str]		    =			(1 - alpha_prod_t_prev) / (1 - alpha_prod_t) * state.common.betas[t]

		if variance_type is None:
			__A :			List[str]		    =			self.config.variance_type

		# hacks - were probably added for training stability
		if variance_type == "fixed_small":
			__A :			int		    =			jnp.clip(__A					,      a_min=1e-2_0							)
		# for rl-diffuser https://arxiv.org/abs/2205.09991
		elif variance_type == "fixed_small_log":
			__A :			Union[str, Any]		    =			jnp.log(jnp.clip(__A					,      a_min=1e-2_0							)							)
		elif variance_type == "fixed_large":
			__A :			List[Any]		    =			state.common.betas[t]
		elif variance_type == "fixed_large_log":
			# Glide max_log
			__A :			Tuple		    =			jnp.log(state.common.betas[t]							)
		elif variance_type == "learned":
			return predicted_variance
		elif variance_type == "learned_range":
			__A :			Union[str, Any]		    =			variance
			__A :			str		    =			state.common.betas[t]
			__A :			Optional[int]		    =			(predicted_variance + 1) / 2
			__A :			List[str]		    =			frac * max_log + (1 - frac) * min_log

		return variance




	def        lowerCAmelCase_       (     self						:     List[str]					,      __A						:     DDPMSchedulerState					,      __A						:     jnp.ndarray					,      __A						:     int					,      __A						:     jnp.ndarray					,      __A						:     Optional[jax.random.KeyArray] = None					,      __A						:     bool = True					,      ):
		__A :			Union[str, Any]		    =			timestep

		if key is None:
			__A :			str		    =			jax.random.PRNGKey(0							)

		if model_output.shape[1] == sample.shape[1] * 2 and self.config.variance_type in ["learned", "learned_range"]:
			__A    ,				__A :			Dict		    =			jnp.split(__A					,      sample.shape[1]					,      axis=1							)
		else:
			__A :			Optional[int]		    =			None

		# 1. compute alphas, betas
		__A :			Union[str, Any]		    =			state.common.alphas_cumprod[t]
		__A :			str		    =			jnp.where(t > 0					,      state.common.alphas_cumprod[t - 1]					,      jnp.array(1.0					,      dtype=self.dtype							)							)
		__A :			str		    =			1 - alpha_prod_t
		__A :			str		    =			1 - alpha_prod_t_prev

		# 2. compute predicted original sample from predicted noise also called
		# "predicted x_0" of formula (15) from https://arxiv.org/pdf/2006.11239.pdf
		if self.config.prediction_type == "epsilon":
			__A :			Any		    =			(sample - beta_prod_t ** 0.5 * model_output) / alpha_prod_t ** 0.5
		elif self.config.prediction_type == "sample":
			__A :			Union[str, Any]		    =			model_output
		elif self.config.prediction_type == "v_prediction":
			__A :			List[str]		    =			(alpha_prod_t**0.5) * sample - (beta_prod_t**0.5) * model_output
		else:
			raise ValueError(
			    F"""prediction_type given as {self.config.prediction_type} must be one of `epsilon`, `sample` """
			    """ for the FlaxDDPMScheduler."""							)

		# 3. Clip "predicted x_0"
		if self.config.clip_sample:
			__A :			Any		    =			jnp.clip(__A					,      -1					,      1							)

		# 4. Compute coefficients for pred_original_sample x_0 and current sample x_t
		# See formula (7) from https://arxiv.org/pdf/2006.11239.pdf
		__A :			Tuple		    =			(alpha_prod_t_prev ** 0.5 * state.common.betas[t]) / beta_prod_t
		__A :			List[Any]		    =			state.common.alphas[t] ** 0.5 * beta_prod_t_prev / beta_prod_t

		# 5. Compute predicted previous sample µ_t
		# See formula (7) from https://arxiv.org/pdf/2006.11239.pdf
		__A :			str		    =			pred_original_sample_coeff * pred_original_sample + current_sample_coeff * sample

		# 6. Add noise
		def random_variance():
			__A :			Dict		    =			jax.random.split(__A					,      num=1							)
			__A :			Dict		    =			jax.random.normal(__A					,      shape=model_output.shape					,      dtype=self.dtype							)
			return (self._get_variance(__A					,      __A					,      predicted_variance=__A							) ** 0.5) * noise

		__A :			Union[str, Any]		    =			jnp.where(t > 0					,      random_variance()					,      jnp.zeros(model_output.shape					,      dtype=self.dtype							)							)

		__A :			Any		    =			pred_prev_sample + variance

		if not return_dict:
			return (pred_prev_sample, state)

		return FlaxDDPMSchedulerOutput(prev_sample=__A					,      state=__A							)




	def        lowerCAmelCase_       (     self						:     Dict					,      __A						:     DDPMSchedulerState					,      __A						:     jnp.ndarray					,      __A						:     jnp.ndarray					,      __A						:     jnp.ndarray					,      ):
		return add_noise_common(state.common					,      __A					,      __A					,      __A							)




	def        lowerCAmelCase_       (     self						:     Optional[int]					,      __A						:     DDPMSchedulerState					,      __A						:     jnp.ndarray					,      __A						:     jnp.ndarray					,      __A						:     jnp.ndarray					,      ):
		return get_velocity_common(state.common					,      __A					,      __A					,      __A							)




	def __len__(     self						:     Any							):
		return self.config.num_train_timesteps






"""simple docstring"""


a				=range(2, 20 + 1)
a				=[10**k for k in range(ks[-1] + 1)]
a				={}





def      lowerCamelCase_					(   __lowerCAmelCase  ,       __lowerCAmelCase  ,       __lowerCAmelCase  ,       __lowerCAmelCase							)				->   Any:




						'''simple docstring'''



						lowerCamelCase__   =sum(a_i[j] for j in range(__lowerCAmelCase  ,       len(__lowerCAmelCase							)							)							)
						lowerCamelCase__   =sum(a_i[j] * base[j] for j in range(min(len(__lowerCAmelCase							)  ,       __lowerCAmelCase							)							)							)

						lowerCamelCase__   , lowerCamelCase__   =0, 0
						lowerCamelCase__   =n - i

						lowerCamelCase__   =memo.get(__lowerCAmelCase							)

						if sub_memo is not None:
												lowerCamelCase__   =sub_memo.get(__lowerCAmelCase							)

												if jumps is not None and len(__lowerCAmelCase							) > 0:
																		# find and make the largest jump without going over
																		lowerCamelCase__   =-1
																		for _k in range(len(__lowerCAmelCase							) - 1  ,       -1  ,       -1							):
																								if jumps[_k][2] <= k and jumps[_k][1] <= max_dn:
																														lowerCamelCase__   =_k
																														break

																		if max_jump >= 0:
																								lowerCamelCase__   , lowerCamelCase__   , lowerCamelCase__   =jumps[max_jump]
																								# since the difference between jumps is cached, add c
																								lowerCamelCase__   =diff + c
																								for j in range(min(__lowerCAmelCase  ,       len(__lowerCAmelCase							)							)							):
																														lowerCamelCase__   , lowerCamelCase__   =divmod(__lowerCAmelCase  ,       10							)
																								if new_c > 0:
																														add(__lowerCAmelCase  ,       __lowerCAmelCase  ,       __lowerCAmelCase							)

												else:
																		lowerCamelCase__   =[]
						else:
												lowerCamelCase__   ={c: []}
												lowerCamelCase__   =sub_memo

						if dn >= max_dn or c + diff >= base[k]:
												return diff, dn

						if k > ks[0]:
												while True:
																		# keep doing smaller jumps
																		lowerCamelCase__   , lowerCamelCase__   =next_term(__lowerCAmelCase  ,       k - 1  ,       i + dn  ,       __lowerCAmelCase							)
																		diff += _diff
																		dn += terms_jumped

																		if dn >= max_dn or c + diff >= base[k]:
																								break
						else:
												# would be too small a jump, just compute sequential terms instead
												lowerCamelCase__   , lowerCamelCase__   =compute(__lowerCAmelCase  ,       __lowerCAmelCase  ,       i + dn  ,       __lowerCAmelCase							)
												diff += _diff
												dn += terms_jumped

						lowerCamelCase__   =sub_memo[c]

						# keep jumps sorted by # of terms skipped
						lowerCamelCase__   =0
						while j < len(__lowerCAmelCase							):
												if jumps[j][1] > dn:
																		break
												j += 1

						# cache the jump for this value digitsum(b) and c
						sub_memo[c].insert(__lowerCAmelCase  ,       (diff, dn, k)							)
						return (diff, dn)





def      lowerCamelCase_					(   __lowerCAmelCase  ,       __lowerCAmelCase  ,       __lowerCAmelCase  ,       __lowerCAmelCase							)				->   List[str]:




						'''simple docstring'''



						if i >= n:
												return 0, i
						if k > len(__lowerCAmelCase							):
												a_i.extend([0 for _ in range(k - len(__lowerCAmelCase							)							)]							)

						# note: a_i -> b * 10^k + c
						# ds_b -> digitsum(b)
						# ds_c -> digitsum(c)
						lowerCamelCase__   =i
						lowerCamelCase__   , lowerCamelCase__   , lowerCamelCase__   =0, 0, 0
						for j in range(len(__lowerCAmelCase							)							):
												if j >= k:
																		ds_b += a_i[j]
												else:
																		ds_c += a_i[j]

						while i < n:
												i += 1
												lowerCamelCase__   =ds_c + ds_b
												diff += addend
												lowerCamelCase__   =0
												for j in range(__lowerCAmelCase							):
																		lowerCamelCase__   =a_i[j] + addend
																		lowerCamelCase__   , lowerCamelCase__   =divmod(__lowerCAmelCase  ,       10							)

																		ds_c += a_i[j]

												if addend > 0:
																		break

						if addend > 0:
												add(__lowerCAmelCase  ,       __lowerCAmelCase  ,       __lowerCAmelCase							)
						return diff, i - start_i





def      lowerCamelCase_					(   __lowerCAmelCase  ,       __lowerCAmelCase  ,       __lowerCAmelCase							)				->   int:




						'''simple docstring'''



						for j in range(__lowerCAmelCase  ,       len(__lowerCAmelCase							)							):
												lowerCamelCase__   =digits[j] + addend
												if s >= 10:
																		lowerCamelCase__   , lowerCamelCase__   =divmod(__lowerCAmelCase  ,       10							)
																		lowerCamelCase__   =addend // 10 + quotient
												else:
																		lowerCamelCase__   =s
																		lowerCamelCase__   =addend // 10

												if addend == 0:
																		break

						while addend > 0:
												lowerCamelCase__   , lowerCamelCase__   =divmod(__lowerCAmelCase  ,       10							)
												digits.append(__lowerCAmelCase							)





def      lowerCamelCase_					(   __lowerCAmelCase = 10**15							)				->   int:




						'''simple docstring'''



						lowerCamelCase__   =[1]
						lowerCamelCase__   =1
						lowerCamelCase__   =0
						while True:
												lowerCamelCase__   , lowerCamelCase__   =next_term(__lowerCAmelCase  ,       20  ,       i + dn  ,       __lowerCAmelCase							)
												dn += terms_jumped
												if dn == n - i:
																		break

						lowerCamelCase__   =0
						for j in range(len(__lowerCAmelCase							)							):
												a_n += digits[j] * 10**j
						return a_n


if __name__ == "__main__":
	print(F'''{solution() = }''')


